course Mth 158 assignment #001001. `Query 1
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00:02:30 query R.1.26 \ was R.1.14 (was R.1.6) Of the numbers in the set {-sqrt(2), pi + sqrt(2), 1 / 2 + 10.3} which are counting numbers, which are rational numbers, which are irrational numbers and which are real numbers?
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RESPONSE --> counting = none rational = 1/2+10.3 irrational = -sqrt(2), pi + sqrt(2) real numbers = -sqrt(2), pi + sqrt(2), 1 / 2 + 10.3
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00:02:42 ** Counting numbers are the numbers 1, 2, 3, .... . None of the given numbers are counting numbers Rational numbers are numbers which can be expressed as the ratio of two integers. 1/2+10.3 are rational numbers. Irrational numbers are numbers which can be expressed as the ratio of two integers. {-sqrt(2)}, pi+sqrt(2) are irrational numbers.. **
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RESPONSE -->
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00:03:44 query R.1.44 \ 32 (was R.1.24) Write in symbols: The product of 2 and x is the product of 4 and 6
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RESPONSE --> 2x=4*6
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00:06:45 query R.1.62 \ 50 (was R.1.42) Explain how you evaluate the expression 2 - 5 * 4 - [ 6 * ( 3 - 4) ]
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RESPONSE --> ok I would work from innermost parenthesis out, multiplying & dividing before addition and subtraction. Addition & subtraction moves left to right. 2 - 5 * 4 - [ 6 * ( 3 - 4) ]= 2 - 5 * 4 - [ 6 * ( -1) ]= 2 - 5 * 4 - [-6 ]= 2- 20 + 6= -18 + 6= -12
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00:06:51 **Starting with 2-5*4-[6*(3-4)]. First you evaluate the innermost group to get 2-5*4-[6*-1] . Then multiply inside brackets to get 2-5*4+6. Then do the multiplication to get 2-20+6. Then add and subtract in order, obtaining -12. **
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RESPONSE --> ok
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00:10:35 query R.1.98 \ 80 (was R.1.72) Explain how you use the distributive property to remove the parentheses from the express (x-2)(x-4).
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RESPONSE --> When implementing the distributive property, you multiply through the first parenthetical expression with the second one. (x-2)(x-4)= (x^2 - 4x) + (-2x - 8)= x^2 - 6x - 8
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00:10:43 ** COMMON ERROR: Using FOIL. FOIL is not the Distributive Law. FOIL works for binomial expressions. FOIL follows from the distributive law but is of extremely limited usefulness and the instructor does not recommend relying on FOIL. Starting with (x-2)(x-4) ; one application of the Distributive Property gives you x(x-4) - 2(x-4) . Applying the property to both of the other terms we get x^2 - 4x - (2x -8). Simplifying: x^2 - 4x - 2x + 8 or x^2 - 6x + 8. *
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RESPONSE --> ok
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00:13:55 query R.1.102 \ 86 (was R.1.78) Explain why (4+3) / (2+5) is not equal to 4/2 + 3/5.
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RESPONSE --> Anytime you are dividing two expressions, it is assumed that the numerator and denominator are enclosed in parentheses -- meaning those expresses are computed first before dividing (4+3) / (2+5)= 7/7= 1
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00:14:55 ** Good answer but at an even more fundamental level it comes down to order of operations. (4+3)/(2+5) means 7/7 which is equal to 1. By order of operations, in which multiplications and divisions precede additions and subtractions, 4/2+3/5 means (4/2) + (3/5), which gives us 2+3/5 = 2 3/5 **
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RESPONSE --> ok
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00:18:53 Query Add comments on any surprises or insights you experienced as a result of this assignment.
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RESPONSE --> insights - I don't recall learning (I am sure I did at some point) the rules for finding values of expressions. It makes it alot easier to discern how to do an equation once you know the rules. comment: it is very hard to do/type equations via a keyboard for assignments for math. It's so much easier to just do them by hand. It's going to take a bit of practice I'm sure.
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